When Is an Outbreak Controlled?

Many countries around the world are struggling with the question of when and how to reopen the country after lockdown.  Many, including the UK and Germany, have come to rely on a parameter called R or R₀ as a benchmark for reopening and staying open.  What makes R so powerful?  In epidemiology, R₀ is the pathogen’s basic reproduction number and represents the number of new infections caused, on average, by a single contagious person.  R, or the effective reproduction number (sometimes designated as R_e or R_t), will start at R₀ and should decline over time as the population gets infected, builds immunity, and mitigation measures are activated. 

R = (1 - P) x R₀,  

where P is the percentage of the population that is immune or out of the pool of susceptible individuals.  If 60% of the population is vaccinated or isolated then only 40% can be infected and R is only 0.4R₀.  R₀ of the novel coronavirus has been variously estimated at between 1.5 and 3.5, with the WHO currently estimating 2.0 to 2.5.  When R is reduced below one, a contagious person can infect just one other person and the number of newly confirmed cases stabilizes and declines, and the outbreak can be short-circuited.  When R₀ is 2.5 the above equation requires that 60% of the population get infected to achieve “herd immunity” to control an outbreak. This does not end the infection which in this example would continue until 88% of the population is infected.  Measuring R₀ is therefore very important but estimating its value, while the pandemic is raging, is problematic and highly model or assumption dependent. 

As an example of the wide range of estimates possible for R, we look at two models.  One of the more interesting infectious disease forecasting website is EpiForecasts which provides models of the COVID-19 pandemic for hundreds of countries and subnational regions including all the states in the US.  They currently estimate R, the effective reproduction number, for the US at 1.04 (with a 90% confidence range of 0.9 to1.2).  A few states such as New Jersey have R < 1, but most states have R >1 such as Florida at 1.1 so their expectation is that case counts will increase as the states reopen.  Their forecasts appear to be slightly more pessimistic than the widely followed IHME model and others who increased case and death count forecasts after states started to reopen two weeks ago.  A few models, such as R_t Covid-19, are more sanguine and estimate a lower R for the US as a whole (~0.85) and R > 1 for only one state, Minnesota.  Their model suggests that the COVID-19 infection is under control in the US and states are safe to open.  Their model for Florida shows a current estimate of 0.89, increasing slightly and with widening uncertainty after the state reopened recently.  

Given this wide variability in estimating R, with one model saying no and another saying yes, we prefer to go back to the original US recommendation for benchmarking safe reopening strategies.  One of its gating criteria simply requires that states demonstrate 14 days of declining confirmed case count.  By this measure, Florida was one of the first of a handful of states to qualify.  Now two weeks later, Florida wants to move on to phase 2.  The figure below shows that as of May 1^st, the state met the criterion for phase 1, and as of May15^th it failed the same criterion to open further.  While we expected this might happen as the state tested more widely, it would seem wiser for the state to proceed more cautiously.  After all, if the outbreak does return, i.e. R > 1, the need to shut down again could cost more in the end.